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October 26th, 2007, 09:54 PM  #1 
Newbie Joined: Oct 2007 Posts: 4 Thanks: 0  Conditional Expectation and Variance Question
Here's the question I'm having trouble with: Show Var[E[YX]] = 0 given random variables X and Y are independent, keeping in mind Var[Y] = Var[E[YX]] + E[Var[YX]]. Here's the work I've done so far. 1) Var[E[YX]] = E[(E[YX])^2]  (E[E[YX]])^2 (using Var[X] = E[X^2]  (E[X])^2) 2) Var[E[YX]] = E[E[YX]^2]  (E[Y])^2 (using E[YX] = E[Y] if X, Y are independent) 3) E[Y]^2  E[Y]^2 (I want to use E[Y] = E[E[YX]] and but I need E[E[YX]^2] = E[E[YX]]^2 What am I missing here? Thanks in advance. 
October 30th, 2007, 01:05 PM  #2 
Member Joined: Nov 2006 From: Vancouver, Canada Posts: 46 Thanks: 0 
Hmm.. That's a silly question your prof gave. I mean E(YX) = E(Y) due to independence, and so E(Y) is just a single number, of course Var(E(Y)) is 0... Did I understand the question wrong? 

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conditional, expectation, question, variance 
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